The worldwide market share for a web browser was 20.5​% in a recent month. Suppose that a sample of 200 random students at a certain university finds that 50 use the browser. Complete parts​ (a) through​ (d) below.

a. At the 0.05 level of​ significance, is there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.5​%?

Determine the null and alternative hypotheses.

A. H0​: π ≤ 0.205​; H1​: π > 0.205

B. H0​: π ≠ 0.205​; H1​: π = 0.205

C. H0​: π ≥ 0.205​; H1​: π < 0.205

D. H0​: π = 0.205​; H1​: π ≠ 0.205

Calculate the test statistic.

ZSTAT = ___? ​(Type an integer or a decimal. Round to two decimal places as​ needed.)

What is the​ p-value?

The​ p-value is ___?. (Type an integer or a decimal. Round to three decimal places as​ needed.)

State the conclusion of the test.

(Reject, Do not reject) the null hypothesis. There is (insufficient, sufficient) evidence to conclude that the market share at the university is (equal to, less than, at least, greater than, at most, not equal to) the worldwide market share of 20.5​%.

b. Suppose that a sample of n = 800 students at the same university​ (instead of n = 200​) determines that 25​% of the sample use the web browser. At the 0.05 level of​ significance, is there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.5​% ?

Calculate the test statistic for the second sample.

ZSTAT = ___? ​(Type an integer or a decimal. Round to two decimal places as​ needed.)

What is the​ p-value for the second​ sample?

The​ p-value is ___? ​(Type an integer or a decimal. Round to three decimal places as​ needed.)

State the conclusion of the test using this second sample at the 0.05 level of significance.

(Do not reject, Reject) the null hypothesis. There is (insufficient, sufficient) evidence to conclude that the market share at the university is (not equal to, at least, equal to, greater than, at most, less than) the worldwide market share of 20.5​%.

c. Compare the results of​ (a) and​ (b) and discuss the effect that sample size has on the​ outcome, and, in​ general, in hypothesis testing. Choose the correct answer below.

A. Increasing the sample size did not affect not being able to reject the null hypothesis.

B. Increasing the sample size did not affect being able to reject the null hypothesis.

C. Increasing the sample size had a major effect on not being able to reject the null hypothesis.

D. Increasing the sample size had a major effect on being able to reject the null hypothesis.

d. What do you think are your chances of rejecting any null hypothesis concerning a population proportion if a sample size of n = 20 is​ used?

The likelihood of rejecting a null hypothesis with n = 20 is relatively (low, high) because (sample proportion decreases, test statistic increases, test statistic decreases, sample proportion increases) as n decreases.